Question

What numbers add to 2 and multiply to -56

Answer 1

-x² + 2x - 56 = 0

Use the quadratic formula to get the roots:


`x = (-b\pm √(b^2-4ac))/(2a)` where the equation is ax² + bx + c =0


`(-b \pm √( b^2 -4( a)(c)) )/(2(a))\\\\ (-2\pm √(2^2 -4(-1)(56)) )/(2(-1))\\ \\(-2\pm √(228 ) )/(-2) = (-2\pm √(4*57 ) )/(-2) \\\\ = (-2\pm 2√(57 ) )/(-2) \\\\ = (-1\pm 1√(57 ) )/(-1) \\\\ =\boxed{\bf{ 1\pm √(57 ) }}\\a`

The two numbers that add up to 2 and multiply to -56 are 1 + √57 and 1 - √57.

Answer 2

The numbers are irrational, so they can't be exactly written down
using only digits.

In exact form, they are

1 + √57
and
1 - √57 .

In rounded form, they are

8.54983
and
-6.54983 .